Question

Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement one by one. The probability that minimum of the two numbers is less than 4, is

• A. $\frac{1}{15}$
• B. $\frac{14}{15}$
• C. $\frac{1}{5}$
• D. $\frac{4}{5}$

Answer 1

The correct option is D $\frac{4}{5}$

Let E be the event that the minimum of the two numbers is less than 4.
Then P(E) = 1 - P(both numbers are greater than or equal to four)
$\Rightarrow P\left(E\right)=1-\frac{3}{6}\times \frac{2}{5}=1-\frac{1}{5}=\frac{4}{5}$